Stanford Cardinal players celebrate their 21-3 win over the California Bears at Memorial Stadium in the 115th annual Big Game Saturday October 20, 2012 in Berkeley California.

Photo: Lance Iversen, The Chronicle

Stanford Cardinal players celebrate their 21-3 win over the...

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BERKELEY, CA - OCTOBER 20: The Stanford Cardinal celebrate with the Axe after beating the California Golden Bears in the "Big Game" at California Memorial Stadium on October 20, 2012 in Berkeley, California. (Photo by Ezra Shaw/Getty Images)

Photo: Ezra Shaw, Getty Images

BERKELEY, CA - OCTOBER 20: The Stanford Cardinal celebrate with...

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Robert Mullins #37 of California causes Stanford Cardinal quarterback Josh Nunes to fumble in the first quarter at Memorial Stadium Saturday October 20, 2012 in the annual 115th Big Game played in Berkeley California.

Photo: Lance Iversen, The Chronicle

Robert Mullins #37 of California causes Stanford Cardinal...

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Stanford's Stepfan Taylor #33 rushes in second half action against the California Bears in the 115th annual Big Game at Memorial Stadium Saturday October 20, 2012 in Berkeley California. Stanford won 21-3.

Photo: Lance Iversen, The Chronicle

Stanford's Stepfan Taylor #33 rushes in second half action against...

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The California Bears run onto the field at Memorial Stadium Saturday October 20, 2012 to face the Stanford Cardinal in the 115th annual Big Game in Berkeley California.

Photo: Lance Iversen, The Chronicle

The California Bears run onto the field at Memorial Stadium...

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Stanford running back Stepfan Taylor (33) runs past California linebacker Nick Forbes during the second half of an NCAA college football game in Berkeley, Calif., Saturday, Oct. 20, 2012. Stanford won 21-3. (AP Photo/Marcio Jose Sanchez)

Photo: Marcio Jose Sanchez, Associated Press

Stanford running back Stepfan Taylor (33) runs past California...

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Stanford Cardinal fans celebrate their 21-3 Big Game victory over the California Bears at Memorial Stadium Saturday October 20, 2012 in Berkeley California.

Photo: Lance Iversen, The Chronicle

Stanford Cardinal fans celebrate their 21-3 Big Game victory over...

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Stanford head coach David Shaw, center, celebrates with linebacker Joe Hemschoot (40) after a 21-3 win over California during an NCAA college football game in Berkeley, Calif., Saturday, Oct. 20, 2012. (AP Photo/Marcio Jose Sanchez)

Photo: Marcio Jose Sanchez, Associated Press

Stanford head coach David Shaw, center, celebrates with linebacker...

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Stanford players celebrate with The Stanford Axe after a 21-3 win over California during an NCAA college football game in Berkeley, Calif., Saturday, Oct. 20, 2012. (AP Photo/Marcio Jose Sanchez)

Photo: Marcio Jose Sanchez, Associated Press

Stanford players celebrate with The Stanford Axe after a 21-3 win...

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BERKELEY, CA - OCTOBER 20: The Stanford Cardinal celebrate with the Axe after beating the California Golden Bears in the "Big Game" at California Memorial Stadium on October 20, 2012 in Berkeley, California. (Photo by Ezra Shaw/Getty Images)

Photo: Ezra Shaw, Getty Images

BERKELEY, CA - OCTOBER 20: The Stanford Cardinal celebrate with...

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BERKELEY, CA - OCTOBER 20: Josh Nunes #6 of the Stanford Cardinal is sacked by Kendrick Payne #96 of the California Golden Bears at California Memorial Stadium on October 20, 2012 in Berkeley, California. (Photo by Ezra Shaw/Getty Images)

Photo: Ezra Shaw, Getty Images

BERKELEY, CA - OCTOBER 20: Josh Nunes #6 of the Stanford Cardinal...

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BERKELEY, CA - OCTOBER 20: Drew Terrell #4 of the Stanford Cardinal tries to avoid being tackled by a diving Jordan Rigsbee #73 of the California Golden Bears at California Memorial Stadium on October 20, 2012 in Berkeley, California. (Photo by Ezra Shaw/Getty Images)

BERKELEY, CA - OCTOBER 20: Zach Ertz #86 of the Stanford Cardinal catches the ball in front of Josh Hill #23 of the California Golden Bears at California Memorial Stadium on October 20, 2012 in Berkeley, California. (Photo by Ezra Shaw/Getty Images)

Photo: Ezra Shaw, Getty Images

BERKELEY, CA - OCTOBER 20: Zach Ertz #86 of the Stanford Cardinal...

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Stepfan Taylor, who gained 189 yards and passed Toby Gerhart for second place on the school's career rushing-yards list, runs by Cal's Deandre Coleman (91) and Josh Hill (23) for a first-quarter touchdown.

Stanford tight end Zach Ertz completes a 68-yard pass play that set up the Cardinal's second score.

Photo: John Storey, Special To The Chronicle

Stanford tight end Zach Ertz completes a 68-yard pass play that set...

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Stanford Cardinal Drew Terrell #4 catches a pass from Josh Nunes and takes it down inside the ten yard line to set up a score in the second quarter against the California Bears in the annual Big Game at Memorial Stadium Saturday October 20, 2012 in Berkeley California.

Photo: Lance Iversen, The Chronicle

Stanford Cardinal Drew Terrell #4 catches a pass from Josh Nunes...

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Stanford's Stepfan Taylor #33 rushes in second half action against the California Bears in the 115th annual Big Game at Memorial Stadium Saturday October 20, 2012 in Berkeley California. Stanford won 21-3.

Photo: Lance Iversen, The Chronicle

Stanford's Stepfan Taylor #33 rushes in second half action against...

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Stanford players with the Axe after they beat Cal 21-3 at Memorial Stadium in Berkeley, Calif., on Saturday, Oct.20th, 2012

With "a big chip on our shoulder" from last week's heartbreaking loss at Notre Dame, No. 22 Stanford took it out on Cal in the first midseason Big Game.

The Cardinal scored three first-half touchdowns, then unleashed their defensive dogs on the Bears on Saturday and held the Pac-12's third-best rushing team to just 3 yards on the ground in 28 attempts.

The 21-3 trouncing in the 115th renewal of the rivalry was so thorough that it sent some of the crowd of 61,024 heading for the exits at Memorial Stadium in the fourth quarter and probably bored a national TV audience throughout the second half.

"The defense played with a big chip on our shoulder from last week; the whole team did," linebacker Chase Thomas said, referring to the 20-13 overtime loss to the Irish that ended with a controversial no-touchdown call on a Stepfan Taylor lunge.

Taylor responded with 189 yards rushing and a touchdown, passed Toby Gerhart for second place on Stanford's all-time career list with 3,616 yards and ensured that the Cardinal would keep the Axe.

Stanford (5-2, 3-1 Pac-12) had four sacks of quarterback Zach Maynard and 11 tackles for loss. The closest Cal came to a touchdown was a short drive to the 4-yard line following a 28-yard punt return by Keenan Allen in the first quarter. But a quarterback draw play was stuffed by Ben Gardner, forcing the Bears to settle for a field goal.

Cal (3-5, 2-3) reached the Stanford 7 in the closing minutes only to have Wayne Lyons pick off Maynard's pass on fourth down. The Bears went without a touchdown in the Big Game for the first time since 1998.

Allen, the third leading receiver in the Pac-12, was held to a season-low four catches for 43 yards and committed a costly fumble.

"Their defense is as good as any defense we have played in this conference for years," Cal coach Jeff Tedford said.

It was a "dominating, suffocating defense," Stanford coach David Shaw said. He said he felt comfortable that his team could thwart the Cal ground game but wondered if it would be able to do it and keep Allen in check at the same time.

"If we had to keep dropping (safeties) down and leaving Allen one-on-one, we were possibly going to give up some big plays," he said. "We were able to do that and still give help over the top on a great football player."

Stanford had to overcome early adversity to record its first road win of the season, take its third straight win in the Cal series and keep its Rose Bowl hopes alive. Quarterback Josh Nunes was stripped of the ball by linebacker Robert Mullins, and Cal's Deandre Coleman recovered. On Stanford's next possession, Jordan Williamson had the first of his two missed field goals.

Nunes regrouped, however, and led Stanford on a short scoring drive that finished with Taylor's 7-yard run, the first touchdown by the Cardinal offense away from Stanford Stadium this year.

"It felt good to get the first touchdown on the road out of our system," Nunes said, "and say, OK, let's go at it and do what we know we can do."

In the second quarter, redshirt freshman quarterback Kevin Hogan came in for what Stanford calls "the Hogan Package." From the wildcat formation, he threw his first career touchdown pass, a 9-yarder to tight end Levine Toilolo. Later in the quarter, after Allen fumbled on a big hit by safety Jordan Richards (who also recovered the ball), Nunes tossed a 20-yard scoring strike to tight end Zach Ertz, ending the day's scoring.

Ertz, who grew up in Bears territory in the East Bay, was left alone in a blown coverage as Stanford started a drive in the second quarter. He grabbed Nunes' throw on the right sideline and raced 68 yards to set up a touchdown.

The key to the win, Ertz said, was "to get Stepfan going. He's the key cog in this offense." And Taylor said it was a matter of pride. "You don't want to be the class that gives the Axe away," he said.